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Partial balance and insensitivity. (English) Zbl 0561.60095
The problems of partial balance and insensitivity are revisited in the context of a discrete state continuous time Markov process $$X=(X_ t).$$
I) Partial balance over a subset A of the state space means that for every $$x\in A$$ the (equilibrium) probability flow from A to x equals the flow from x to A.
II) Insensitivity of the steady state distribution of X ”to nominial sojourn time in A” states that the distribution of the nominal sojourn time in A may be changed without effecting the steady state if the mean sojourn time in A remains invariant.
The author shows that property I) holds if and only if II) holds, and gives a multiset version of this theorem. The paper is part of a sequence of articles which consider insensitivity and partial (or local) balance. (See the references.) Its advantage is that the standard terminology of Markov processes is used.